Rules Only: V=AxT and S=0.5xAxT^2

[AnotherDilbert]

On the playing surface you have to track displacement because you have to know where stuff is so they can interact.

If you plot velocity vector then you can not get range to target without doing a bit of maths.

I have no idea what you mean.

The position of the dot or miniature representing the ships gives us the range, we can physically measure it on the playing surface, without involving any vectors at all.

The ship's vector (originating in the ship's position, pointing at the future) is its velocity. The vector is not involved in measuring the current range. The vector shows what will happen next movement phase, barring any acceleration.

It's explicit in LBB2:

LBB2'81, p26, "Basic Parameters":
_ _ 3. Thrust: Maneuver drive thrust is measured in Gs (gravities) expressed as a vector of both length and direction. While direction is variable, the length of the arrow is represented at the scale 100 mm equals 1 G (1,000 seconds acceleration at 1 G will produce a velocity change of 10,000 km, or 100 mm in scale, per turn).

A burn of 1 G for 1 turn = 10 m/s² for 1000 s = 10 000 m/s = 10 km/s, it's a velocity change, acceleration.
The resulting vector is 10 000 km/turn = 10 000km/1 000 s = 10 km/s, it's a velocity.

Without any other acceleration the ship will travel the same 10 000 km/turn, every turn, forever. The ship's position will change every turn, the vector (the velocity) will move with the ship, but remain constant length and direction.

A basic application of Newton's Laws of Motion.


I have no idea what of the above you disagree with, but it must be something, probably fundamental. Please enlighten me?

 

[mike wightman]

Ok try again

Start at 0 "vector"

Despite what the game says the vector we draw is its displacement, it is not its velocity - the quote shows this.
"expressed as a vector of both length and direction."

accelerate for1g for one turn
what is your velocity?
what is your displacement?

Now just keep accelerating for another turn, what is your displacement, what is your velocity?

Which one do you draw on the map to show your current position...

your "velocity vector" is not the same as your "displacement vector"

 

[AnotherDilbert]

Ok try again

OK.

Start at 0 "vector"

Despite what the game says the vector we draw is its displacement, it is not its velocity - the quote shows this.
"expressed as a vector of both length and direction."

Both length and direction from a starting point is the definition of a vector, whether it describes a position, a velocity, or an acceleration.
https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)#Vectors_in_Euclidean_geometry

accelerate for1g for one turn
what is your velocity?
what is your displacement?

Start at P₀ with velocity 0, vector of length 0.
Turn 1: Accelerate, and move to P₁, move the vector with the ship.
Turn 2: No acceleration, velocity unchanged, move to P₂, move the vector with the ship.

The "displacement" is the position.
The vector is the velocity (black vector).
Constant velocity means the position points are evenly spaced.

Now just keep accelerating for another turn, what is your displacement, what is your velocity?

Start at point P₀ with velocity 0, vector of length 0.
Turn 1: Accelerate, and move to point P₁, move the vector with the ship.
Turn 2: Accelerate, and move to point P₃, move the vector with the ship.

With two turns of acceleration the velocity vector is twice as long, and we have moved 50% further (1 unit the first turn, 2 units the second turn = 3 units).
Constant acceleration means the position points are further and further apart, the ship is going faster and faster.

Which one do you draw on the map to show your current position...

The velocity vector starts at your current position, and points forward. It shows both your current position and your velocity.

your "velocity vector" is not the same as your "displacement vector"

There is no "displacement vector", just a position, a point; the origin of your velocity vector.

Mayday, p4:
_ _ A. The past position counter is moved to the hex containing the present ship position counter.
_ _ B. The present ship position counter is moved to the hex containing the future ship position counter.
_ _ C. A line is visualized from the past position counter to the present position counter; it is then extended in the same direction for an equal distance, and the future position counter is placed in the hex at the end of that line. This indicates the predicted position of the ship next turn, ...

Move the ship, and the vector with it.

LBB2'81, p27:
Each ship has a vector, which expresses that ship's velocity as a line (arrow) of a specific direction. For example, a ship might have a vector of 150 mm at 90 degrees, or of 100 mm at 277 degrees. It is possible to have a vector of 0 mm ,whereupon the direction becomes irrelevant because the ship is stationary.

The ship has a velocity vector, it points from the ship in the direction of travel.
https://en.wikipedia.org/wiki/Velocity

Here an object in two positions on the light green line of travel.
The velocity vector v (medium green) points from the current position of the object forward, in the direction of travel.
The acceleration (dark green) is the change of the velocity vector.
AKA Newtonian mechanics.

 

[Spinward Flow]

Despite what the game says the vector we draw is its displacement, it is not its velocity - the quote shows this.
"expressed as a vector of both length and direction."

Somebody really doesn't understand how vectors work as a fundamental concept of Newtonian Motion Physics.

There are plenty of basic physics tutorials available on youtube that can clarify this fundamental misunderstanding.

 

[atpollard]

My take is: If we want to make the vector system usable, we have to make it simpler...

That I can agree with ... unfortunately, vector movement in orbital space does not naturally lend itself to "simpler".

Mayday did a better than average job.

 

[mike wightman]

Somebody really doesn't understand how vectors work as a fundamental concept of Newtonian Motion Physics.

There are plenty of basic physics tutorials available on youtube that can clarify this fundamental misunderstanding.

You had better go and read them then.
Then you may be able to offer something constructive.

 

[AnotherDilbert]

That I can agree with ... unfortunately, vector movement in orbital space does not naturally lend itself to "simpler".

That's the challenge: If we can't make it simpler, we can't make it actually usable...

Perhaps we could start with missiles, like in MgT2 they could just arrive at the target a few rounds later, no vector manoeuvring needed? That would make missiles usable at longer range and massively decrease workload per turn. (Just assume the missile gunner knows what he's doing.)

Mayday did a better than average job.

Mayday is almost the same as LBB2, apart from applying acceleration at the end of the turn and only having one gravity band?

 

[mike wightman]

OK.


Both length and direction from a starting point is the definition of a vector.
https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)#Vectors_in_Euclidean_geometry



Start at P₀ with velocity 0, vector of length 0.
Turn 1: Accelerate, and move to P₁, move the vector with the ship.
Turn 2: No acceleration, velocity unchanged, move to P₂, move the vector with the ship.
View attachment 3614
The "displacement" is the position.
The vector is the velocity (black vector).
Constant velocity means the position points are evenly spaced.


Start at point P₀ with velocity 0, vector of length 0.
Turn 1: Accelerate, and move to point P₁, move the vector with the ship.
Turn 2: Accelerate, and move to point P₃, move the vector with the ship.
View attachment 3615
With two turns of acceleration the velocity vector is twice as long, and we have moved 50% further (1 unit the first turn, 2 units the second turn = 3 units).
Constant acceleration means the position points are further and further apart, the ship is going faster and faster.




The velocity vector starts at your current position, and points forward. It shows both your current position and your velocity.


There is no "displacement vector", just a position, a point; the origin of your velocity vector.



Move the ship, and the vector with it.


The ship has a velocity vector, it points from the ship in the direction of travel.
https://en.wikipedia.org/wiki/Velocity

Here an object in two positions on the light green line of travel.
The velocity vector v (medium green) points from the current position of the object forward, in the direction of travel.
The acceleration (dark green) is the change of the velocity vector.
AKA Newtonian mechanics.

A vector is a quantity with a magnitude and direction. Force is a vector quantity , velocity is a vector quantity, as are acceleration, velocity and displacement.

You can not add a velocity vector to a force vector, you can only add like with like.

What we draw on the board is the displacement, what you represent with the "vector" arrows are past present and future positions, not velocities.

You didn't answer my questions by using the equations, rather you continue to draw velocity vectors rather than displacement vectors.

You can draw velocity vectors, but they do not give you a position they give you a relative velocity, similarly you can draw force vectors, or acceleration vectors, what you can't do is mix and match.

A ship that starts with a velocity of 0 and accelerates at 1g (10m/s)for 1000s.

How far has it moved? This is what we should draw 5,000,000m

What is the change to its velocity? It starts at 0 and ends with 10,000m/s

 

[kilemall]

I don’t understand the missile complaint. At most you will have 3 courses per round, the optimal course for current target accel, one behind and one ahead. Most missiles would be in the main group. Done.

I do want to track on missile/target relative vee for damage purposes, plus potential avoidance.

 

[Spinward Flow]

You can not add a velocity vector to a force vector, you can only add like with like.

/facepalm

What we draw on the board is the displacement, what you represent with the "vector" arrows are past present and future positions, not velocities.

The horror FAIL ... the horror FAIL ...

You didn't answer my questions by using the equations

Actually, the equations DO answer your questions, just not the way you want the answers to be ... but admitting that would be damaging ... so ...

A ship that starts with a velocity of 0 and accelerates at 1g (10m/s)for 1000s.
How far has it moved? This is what we should draw 5,000,000m
What is the change to its velocity? It starts at 0 and ends with 10,000m/s

Acceleration IS NOT Velocity IS NOT Distance.
Stop trying to conflate these 3 different concepts into a single idea that transcends everything.

 

[AnotherDilbert]

A vector is a quantity with a magnitude and direction. Force is a vector quantity , velocity is a vector quantity, as are acceleration, velocity and displacement.

Agreed.

You can not add a velocity vector to a force vector, you can only add like with like.

You integrate the acceleration over t, in effect multiplying with t, to get the velocity change during time t.
1 G for 1 turn = 1 Gturn.
10 m/s² for 1000 s = 10 000 m/s a velocity = 100 mm/turn.

What we draw on the board is the displacement, what you represent with the "vector" arrows are past present and future positions, not velocities.

No, not in Newtonian mechanics, nor LBB2.

LBB2'81, p27:
Each ship has a vector, which expresses that ship's velocity as a line (arrow) of a specific direction.

Please don't just say LBB2 is wrong (again).

You didn't answer my questions by using the equations, rather you continue to draw velocity vectors rather than displacement vectors.

a = 1 G. constant acceleration. (vector often denoted by bold).
da/dt = v(t) = at + v₀. velocity increases linearly with time for constant acceleration.
dv/dt = d(t) = ½at² + v₀t + d₀. distance travelled increases with square of the time.

Which gives us the travel formulae, if we assume v₀ = 0 and d₀ = 0.

This isn't exactly true for LBB2, but reasonably good, as:

LBB2'77, p37:
The vector movement system used in this game assumes, for simplicity, that all acceleration is instantaneous, and occurs at the beginning of the movement phase of the turn. For those who wish a greater degree of realism, note that, if acceleration occurs evenly during the movement phase, initial movement (i.e., during the turn acceleration is applied) will only be half that of the added vector (D = ½at² for constant a). Full effect of the new vector will be felt only on succeeding turns.

That is just another way of describing Newtonian mechanics. Is that formulae enough?

You can draw velocity vectors, but they do not give you a position they give you a relative velocity, similarly you can draw force vectors, or acceleration vectors, what you can't do is mix and match.

The velocity vectors are not relative, they are absolute (in Newton). They give both position and velocity, as they always start in the current position of the ship.

A ship that starts with a velocity of 0 and accelerates at 1g (10m/s)for 1000s.

Acceleration is measured in m/s², not m/s.
You get change in velocity over a time by integrating over time (=multiplying with time for constant acceleration), thereby turning it into a change of velocity, measured in m/s the dimension of velocity.

How far has it moved? This is what we should draw 5,000,000m

What is the change to its velocity? It starts at 0 and ends with 10,000m/s

So, the velocity vector starts at the new position, and points 1 Gturn in the direction of travel.
The velocity vector give both position and velocity, as they always start in the current position of the ship.

Like this:


Yes, LBB2 will give an inexact answer as all acceleration "this game assumes, for simplicity, that all acceleration is instantaneous, and occurs at the beginning of the movement phase of the turn". LBB2 says P₁ is 100 mm = 10 000 km away from P₀, and P₃ is 200 mm away from P₁ and 300 mm away from P₀.

Constant acceleration 1 G [100 mm/turn/turn], starting velocity 0 m/s [0 mm/turn].
Turn 1: Velocity is 10 000 m/s [100 mm/turn] the whole turn, so we have travelled 10 000 m/s × 1 000 s = 10 000 km [100 mm].
Turn 2: Velocity is 20 000 m/s [200 mm/turn] the whole turn, so we have travelled 20 000 m/s × 1 000 s = 20 000 km [200 mm] this turn, for a total of 30 000 km [300 mm].


If we were exact P₁ would be 50 mm = 5 000 km away from P₀, and P₃ would be 150 mm away from P₁ and 200 mm away from P₀.

d(t) = ½at²
d(0) = 0 km
d(1 turn = 1000 s) = 5 000 km [50 mm in scale].
d(2 turns = 2000 s) = 20 000 km [200 mm in scale] totally, 15 000 km [150 mm] this turn.

 

[whartung]

The discrepancy is real, but does not impact play. Simply, the complexity of managing it isn't worth the loss of it during play.

I wrote this mechanic when dabbling with it on my computer, and it really doesn't make enough difference to matter.

The Traveller game mechanics aren't that sensitive to position and range to make the case where it would come into play that meaningful.

 

[AnotherDilbert]

The discrepancy is real, but does not impact play. Simply, the complexity of managing it isn't worth the loss of it during play.

I wrote this mechanic when dabbling with it on my computer, and it really doesn't make enough difference to matter.

Agreed.

 

[AnotherDilbert]

What we draw on the board is the displacement, what you represent with the "vector" arrows are past present and future positions, not velocities.

The velocity vector starts in the current position, and points in the direction of travel. We will only ever go the end of the velocity vector if we don't add any acceleration whatsoever.

The velocity vector does not point to the next future position, just a possible future position.

In the constant acceleration example above we would not go to P4 the end of the velocity vector, but P5, a new point:


This velocity vector only describes one ship. If we have several ships, each ship will have its own vector.

 

[mike wightman]

/facepalm

The horror FAIL ... the horror FAIL ...

Actually, the equations DO answer your questions, just not the way you want the answers to be ... but admitting that would be damaging ... so ...

Acceleration IS NOT Velocity IS NOT Distance.
Stop trying to conflate these 3 different concepts into a single idea that transcends everything.

I'm not, I am the one arguing for keeping them separates and not mixing them up erroneously.

Take the time to read, understand, and possibly even learn and you may one day be able to join in - but up to now all you do is display your rudeness and lack of any actual understanding.

 

[Spinward Flow]

Take the time to read, understand, and possibly even learn and you may one day be able to join in - but up to now all you do is display your rudeness and lack of any actual understanding.

@mike wightman ... there are limits to patience and to understanding that can be offered to someone who resolutely refuses to accept answers when they are provided, demonstrated and even proven, both mathematically and graphically ... on a repeating basis.

 

[atpollard]

Mayday is almost the same as LBB2, apart from applying acceleration at the end of the turn and only having one gravity band?

By setting the scale of 1 Hex equal to the "Thrust Vector" for 1 turn at 1G, they completely removed the all THRUST VECTORS from the plotting and calculations on the game map. After the Velocity and Gravity vectors determine a new movement position, the ship's THRUST may simply change the position 1 hex in any direction for each G of Performance (select any hex within 2 hexes for a 2G ship). That was a VERY elegant solution in my opinion that greatly simplified the game mechanics and improved playability.

The direction of Gravity vectors was simplified to the 6 directions of a Hex face from the infinite number of degrees in the LBB2 fractional degree system, which further sped the application of gravity vectors in game play (they just stepped in increments of a whole hex in easy to identify directions.) Conforming movement to discrete hexes made it more like a chess board [knight moves one forward and one diagonal] and less like a HS Geometry test [now get out your protractors and draw the following three vectors ...].

I believe in concept Mayday was very like LBB2, but in execution Mayday was very much improved.

 

[atpollard]

The discrepancy is real, but does not impact play. Simply, the complexity of managing it isn't worth the loss of it during play.

I wrote this mechanic when dabbling with it on my computer, and it really doesn't make enough difference to matter.

The Traveller game mechanics aren't that sensitive to position and range to make the case where it would come into play that meaningful.

Probably true given Traveller ranges [something places like Project Rho have mentioned are an unrealistic but common Sci-Fi trope]. I think FF&S touched on Lasers and "Grav Focusing" ranges vs "Realistic" ranges.

I think the ultimate conclusion for Sci-Fi and RPGs is "realistic is boring".
"Your fragile as an egg shell Starship spends 29 days on a minimum energy transfer orbit and arrives at the 100 Diameter jump limit." is just not what most people are looking for.

 

[mike wightman]

@mike wightman ... there are limits to patience and to understanding that can be offered to someone who resolutely refuses to accept answers when they are provided, demonstrated and even proven, both mathematically and graphically ... on a repeating basis.

You have yet to provide a single answer, all you do is regurgitate spurious half understandings and shout a lot. Not to mention the constant rudeness, personal attacks and just basic deliberate unpleasantness.

1. explain without shouting what we actually draw on the game board according to the rules.
2. if the "vectors" are velocity vectors then you do not know the positions of ships
3. if the "vectors" show position - which they must to allow for weapon range- then they are displacement.

Ships in miniature combat move using their maneuver drive (M-Drive); use of
the J-Drive exits a ship into interstellar space, out of the area of play. Maneuver drive
uses thrust to accelerate a ship in a specific direction for a specified distance. This
direction and distance is expressed as an arrow (a line in one direction) called a vector.
Vectors determine how far, and in what direction, a ship can travel.

Distance and direction - a displacement vector.
Not force, not acceleration, not momentum, not velocity - direction and distance is displacement. QED

Note that the very next sentence proves the authors didn't understand the physics of it since they then say.

Each ship has a vector, which expresses that ship's velocity as a line (arrow) of a
specific direction

This directly contradicts the first definition given.

This is the source of the confusion, the rules claim on the one hand that we draw a displacement vector, and then the other that we draw a velocity vector. This requires either two different coloured lines or the velocity vector being noted on the ship display.

 

[RogerD]

A few observations:
1. I learned vector math from Traveller. Also, the basic Newtonian motion equations. I often miss them in editions of Traveller after Classic.
2. I never quite realized that the 0.5 was missing from the Classic Traveller '81 Space Combat rules I had. I sort of thought there was something special about the choice of scales that made it work out. Oh well!
3. I had done some reasoning about this thinking about T5 scales a while back. There was a recent similar thread over here (linking into the middle of the thread to some thoughts I had specifically about space combat scale).
4. The worst physics in all of Traveller is this rule from MegaTraveller:

Each unit must specify a movement speed to be used for the turn. The movement speed represents the maximum number of squares the unit can move that turn, however, the unit may move any number of squares less than the maximum, or it may even remain stationary (25,000 km per square is a lot of space-in effect, the unit is circling in the square)

Not only are those terrible physics, but it implies every ship should just accelerate to the max every turn to have maximum flexibility for future turns, making it bad game mechanics.